A note on dictatorship, liberalism and the Pareto rule

Abstract

This note presents a short comment and explanation of the approach and results presented in my previous papers published in this journal. I have divided the traditional social choice axioms, introduced by Kenneth Arrow and Amartya Sen, into two classes, based on their linguistic and mathematical complexity. The first class consists of ‘the unrestricted domain’ and ‘the independence of irrelevant alternatives’, (Arrow, 1963; (Sen, 1970b;Maskin, 2020), which need a higher-order language, and can be treated as meta-axioms. The second class contains a group of linguistically simpler axioms, such as ‘dictatorship’, ‘liberalism’ and ‘the Pareto rule’. Naturally, it is possible to make an easier logical analysis of the deductive properties and relationships between the axioms belonging to the second class, and the paper explains a method for their simplification. The basic conclusion is that after these simplifications, we obtain a fragment of the traditional Arrow-Sen theory in which we can also prove well-known impossibilities, including the counterparts of Arrow’s and Sen’s theorems. I consider that the value of each simplified approach lies in providing an opportunity to a wider circle of readers to better understand the basic ideas, results and spirit of traditional Social Choice Theory.

Keywords

• impossibility theorems
• social choice theory
• dictatorship
• liberalism
• pareto rule